1. Field of the Invention
The invention relates to a fuel injection amount control apparatus for an internal combustion engine, which controls a fuel injection amount on the basis of an output value of an air-fuel ratio sensor (a downstream side air-fuel ratio sensor) disposed downstream of a catalyst that is provided in an exhaust passage of the internal combustion engine.
2. Description of Related Art
As shown in FIG. 1, a typical fuel injection amount control apparatus for an internal combustion engine includes a catalyst (a three-way catalyst) 43 disposed in an exhaust passage of the engine, an upstream side air-fuel ratio sensor 56, and a downstream side air-fuel ratio sensor 57. The upstream side air-fuel ratio sensor 56 and the downstream side air-fuel ratio sensor 57 are disposed upstream and downstream of the catalyst 43, respectively.
An output value Vabyfs of the upstream side air-fuel ratio sensor 56 varies relative to an air-fuel ratio (an upstream side air-fuel ratio abyfs) of a detected gas in a manner shown in FIG. 2.
An output value Voxs of the downstream side air-fuel ratio sensor 57 varies relative to an air-fuel ratio (a downstream side air-fuel ratio afdown) of the detected gas in the manner shown in FIG. 3. More specifically, the output value Voxs takes a maximum output value max when the air-fuel ratio of the detected gas is richer than a stoichiometric air-fuel ratio and takes a minimum output value min when the air-fuel ratio of the detected gas is leaner than the stoichiometric air-fuel ratio. The output value Voxs varies rapidly from the minimum output value min to the maximum output value max when the air-fuel ratio of the detected gas varies from a leaner air-fuel ratio than the stoichiometric air-fuel ratio to a richer air-fuel ratio than the stoichiometric air-fuel ratio, and varies rapidly from the maximum output value max to the minimum output value min when the air-fuel ratio of the detected gas varies from a richer air-fuel ratio than the stoichiometric air-fuel ratio to a leaner air-fuel ratio than the stoichiometric air-fuel ratio.
The fuel injection amount control apparatus calculates a “correction amount of the fuel injection amount” for aligning the air-fuel ratio (the upstream side air-fuel ratio abyfs) expressed by the output value of the upstream side air-fuel ratio sensor with a “target air-fuel ratio set at the stoichiometric air-fuel ratio”. The correction amount will also be referred to as a main feedback amount. Air-fuel ratio feedback control using the main feedback amount will be referred to as main feedback control.
Further, the fuel injection amount control apparatus calculates a “correction amount of the fuel injection amount” separately from the main feedback amount” on the basis of a “difference (also referred to as an “output deviation” hereafter) between the output value of the downstream side air-fuel ratio sensor and a downstream side target value set at a value substantially corresponding to the stoichiometric air-fuel ratio”. This correction amount will also be referred to as a sub-feedback amount. Air-fuel ratio feedback control using the sub-feedback amount will be referred to as sub-feedback control. The fuel injection amount control apparatus then corrects the fuel injection amount using the main feedback amount and the sub-feedback amount, whereby the air-fuel ratio of an air-fuel mixture supplied to the engine is controlled to the stoichiometric air-fuel ratio. Note that the air-fuel ratio of the air-fuel mixture supplied to the engine will also be referred to as the air-fuel ratio of the engine, and is substantially equal to the air-fuel ratio of exhaust gas flowing into the catalyst 43.
The sub-feedback amount is calculated through PI control or PID control, and therefore includes at least a proportional term and an integral term. More specifically, the fuel injection amount control apparatus calculates the proportional term of the sub-feedback amount by multiplying a proportional gain by the output deviation. The fuel injection amount control apparatus calculates a time integrated value by integrating a value obtained by multiplying an adjustment gain by the output deviation, and calculates the integral term of the sub-feedback amount on the basis of the time integrated value.
Incidentally, a steady state error occurs in the target air-fuel ratio of the air-fuel ratio of the engine due to an intake air amount detection error by an air flow meter, individual differences or temporal deterioration in an injection characteristic of a fuel injection valve, an air-fuel ratio detection error by the upstream side air-fuel ratio sensor, and so on (to be referred to collectively hereafter as an “intake/exhaust system error”). Accordingly, the intake/exhaust system error appears in the time integrated value. In other words, the time integrated value converges on an identical value to a value expressing the magnitude of the intake/exhaust system error. Therefore, the fuel injection amount control apparatus is able substantially to align the air-fuel ratio of the engine with the stoichiometric air-fuel ratio even when an error occurs in the intake/exhaust system.
However, a predetermined amount of time is required for the time integrated value to converge. Moreover, during a “period in which a sub-feedback control condition (downstream side feedback condition) is not established” such as when the downstream side air-fuel ratio sensor is not active, for example, the time integrated value is not updated. Hence, the fuel injection amount control apparatus obtains the time integrated value (or the “integral term of the sub-feedback amount”, which is a value that correlates with the time integrated value) as a learned value (a sub-feedback (FB) learned value) of the sub-feedback amount at intervals of a predetermined learning interval time Tth.
The learning interval time Tth is longer than an update interval time of the sub-feedback amount (and therefore the time integrated value). The sub-FB learned value is stored in a “backup random access memory (RAM) or the like capable of holding data even when the engine is inoperative”. Further, the fuel injection amount control apparatus controls the fuel injection amount using the sub-FB learned value during the period in which the sub-feedback control condition is not established, and when the sub-feedback control condition is established, the fuel injection amount control apparatus uses a value corresponding to the sub-FB learned value as an initial value of the time integrated value. Hence, during the period in which the sub-feedback control condition is not established, the fuel injection amount can be controlled to an optimum value. Furthermore, the time integrated value can be set at an appropriate value immediately after the sub-feedback control condition is established.
The sub-FB learned value may diverge greatly from an intended convergence value. The intended convergence value of the sub-FB learned value is a value expressing the magnitude of the error in the intake/exhaust system, and will be referred to as a “convergence value” hereafter. For example, the sub-FB learned value may diverge greatly from the convergence value when the sub-FB learned value stored in the backup RAM is cleared due to battery replacement or the like. The sub-FB learned value may also diverge greatly from the convergence value when a misfire rate of the engine varies, when the fuel injection characteristic of the fuel injection valve in a specific cylinder differs greatly from the fuel injection characteristic of the fuel injection valves in another cylinder, and so on. FIG. 4A shows an outline of the manner in which the sub-FB learned value gradually converges from a state of diverging greatly from the convergence value.
The fuel injection amount control apparatus modifies a “variation speed of the time integrated value” in accordance with a degree of convergence of the sub-FB learned value so that the sub-FB learned value converges with the convergence value quickly. More specifically, when a variation amount (an amount of change) of the sub-FB learned value within a predetermined period exceeds a predetermined width, the fuel injection amount control apparatus determines that the sub-FB learned value has not converged, and therefore increases an amount by which the time integrated value is updated per update. When the variation amount of the sub-FB learned value within the predetermined period does not exceed the predetermined width, on the other hand, the fuel injection amount control apparatus determines that the sub-FB learned value has converged, and therefore reduces the amount by which the time integrated value is updated per update. As a result, the sub-FB learned value can be brought close to the convergence value quickly when the sub-FB learned value has not converged, and excessive variation in the sub-FB learned value due to disturbances can be avoided when the sub-FB learned value has converged (see Japanese Patent Application Publication No. 2009-162139 (JP-A-2009-162139), for example). by modifying the update amount of the time integrated value per update in this manner, it is important to determine whether or not the learned value has converged with a high degree of precision in order to set the “update amount of the time integrated value per update” at an appropriate value. Even with an apparatus that does not modify the update amount of the time integrated value per update, it is important to determine whether or not the sub-FB learned value has converged with a high degree of precision in an “apparatus that obtains a degree of unevenness among air-fuel ratios of respective cylinders on the basis of a value that correlates with the sub-FB learned value” or the like (see Japanese Patent Application Publication No. 2009-30455 (JP-A-2009-30455), for example).
As shown in FIG. 4B, a variation amount of the sub-FB learned value varies substantially depending on the magnitude of “the proportional term of the sub-feedback amount” in a situation where the sub-FB learned value is substantially converged.
More specifically, in FIG. 4B, a “proportional gain for calculating the proportional term of the sub-feedback amount” within a period extending from a time t0 to a time t4 is set at substantially double the proportional gain from the time t4 onward. The proportional term of the sub-feedback amount is a “product of the output deviation and the proportional gain”. In accordance with the characteristics of the downstream side air-fuel ratio sensor 57, the output value Voxs of the downstream side air-fuel ratio sensor 57 substantially takes either “the maximum output value max or the minimum output value min”, and the downstream side target value is substantially unchanging. Therefore, the magnitude of the output deviation is substantially constant. Hence, the magnitude of the proportional term of the sub-feedback amount within the period from the time t0 to the time t4 is substantially double the magnitude of the proportional term from the time t4 onward. Meanwhile, the integral term of the sub-feedback amount is substantially converged, and therefore the air-fuel ratio of the gas flowing into the catalyst 43 varies substantially on the basis of the proportional term of the sub-feedback amount.
Hence, a “reduction speed of an oxygen storage amount OSA of the catalyst 43” from the time t0 to a time t1 and from a time t2 to a time t3 is double the reduction speed of the oxygen storage amount OSA from the time t4 to a time t5 and from a time t6 to a time t7. Similarly, an “increase speed of the oxygen storage amount OSA of the catalyst 43” from the time t1 to the time t2 and from the time t3 to the time t4 is double the increase speed of the oxygen storage amount OSA from the time t5 to the time t6 and from the time t7 to a time t8.
Meanwhile, the output value Voxs of the downstream side air-fuel ratio sensor 57 varies from the minimum output value min to the maximum output value max when the oxygen storage amount OSA of the catalyst 43 reaches “0” such that rich gas flows out from the catalyst 43, and varies from the maximum output value max to the minimum output value min when the oxygen storage amount OSA of the catalyst 43 reaches a maximum oxygen storage amount Cmax (a maximum value of the amount of oxygen that can be stored by the catalyst 43) such that lean gas flows out from the catalyst 43.
As a result, an inversion period (a time required to vary to the minimum output value min after varying from the minimum output value min to the maximum output value max and then to vary back to the maximum output value max) of the output value Voxs of the downstream side air-fuel ratio sensor 57 is substantially inversely proportionate to the proportional gain. In other words, the inversion period during the period from the time t0 to the time t4 is ½ the inversion period during the period from the time t4 to the time t8.
The time integrated value and the integral term of the sub-feedback amount, meanwhile, vary substantially in proportion with a length of the inversion period, and therefore the sub-FB learned value also varies substantially in proportion with the length of the inversion period. Hence, a variation amount (variation width) D1 of the sub-FB learned value during the period from the time t4 to the time t8 is double a variation amount D2 of the sub-FB learned value during the period from the time t0 to the time t4.
As is evident from the above description, by setting the proportional gain to take a large value when the sub-FB learned value is in a substantially converged condition, the variation amount of the sub-FB learned value can be reduced. In other words, setting the proportional gain at a large value is useful for determining early that the sub-FB learned value has converged.
However, NOx and unburned material are discharged from the catalyst 43 every time the oxygen storage amount OSA of the catalyst 43 reaches the “maximum oxygen storage amount Cmax” and “0”, respectively. Therefore, when the proportional gain remains set at a large value even after the sub-FB learned value is determined to have converged, the frequency with which NOx and unburned material are discharged increases, which is undesirable in terms of reducing emissions.